Question

Two thermometers x and y have fundamental intervals of 80 ∘ and 120 ∘ . When immersed in ice, they show the readings of 20 ∘ and 30 ∘ . If y measures the temperature of a body as 120 ∘ , the reading of x is :

• A. 60
• B. 80
• C. 100
• D. 120

Answer 1

Answer: (B)

80

Answer 2

1. Determine the steam point for each thermometer:

   • Thermometer X: Ice point = $20^\circ$, Fundamental interval = $80^\circ$. Steam point = $20^\circ + 80^\circ = 100^\circ$.
   • Thermometer Y: Ice point = $30^\circ$, Fundamental interval = $120^\circ$. Steam point = $30^\circ + 120^\circ = 150^\circ$.

2. Use the linear scale conversion formula: $\frac{T_X - T_{X, \text{ice}}}{T_{X, \text{steam}} - T_{X, \text{ice}}} = \frac{T_Y - T_{Y, \text{ice}}}{T_{Y, \text{steam}} - T_{Y, \text{ice}}}$

3. Substitute known values and solve for $T_X$: $\frac{T_X - 20}{100 - 20} = \frac{120 - 30}{150 - 30}$ $\frac{T_X - 20}{80} = \frac{90}{120} = \frac{3}{4}$ $T_X - 20 = 80 \times \frac{3}{4} = 60$ $T_X = 60 + 20 = 80^\circ$